In this article, an alternative approach to detecting the computation completion of combinatorial blocks in asynchronous digital systems is presented. The proposed methodology is based on well-known phenomenon that occurs in digital systems fabricated in CMOS technology. Such logic circuits exhibit significantly higher current consumption during the signal transitions than in the idle state. Duration of these current peaks correlates very well with the actual computation time of the combinatorial block. Hence, this fact can be exploited for separation of the computation activity from static state. The paper presents fundamental background of addressed alternative completion detection and its implementation in single-rail encoded asynchronous systems, the proposed current sensing circuitry, achieved simulation results as well as the comparison to the state-of-the-art methods of completion detection. The presented method promises the enhancement of the performance of an asynchronous circuit, and under certain circumstances it also reduces the silicon area requirements of the completion detection block.